Testinar Grade 7 math

Factoring Expressions

Students will build Grade 7 mastery of factoring expressions using models, equations, and test-style reasoning.

CH04-04 Expressions

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

What is the GCF of \(4\) and \(6\)?
1. \(2\)
2. \(4\)
3. \(6\)
4. \(24\)
Which expression shows \(2 \cdot 5 + 2 \cdot 3\) factored?
1. \(2(5+3)\)
2. \((2+5)(2+3)\)
3. \(2 \cdot 15\)
4. \(5+3\)
Factor the expression: \(6x+18\)
1. \(6(x+3)\)
2. \(3(2x+6)\)
3. \(2(3x+9)\)
4. \(6(x+18)\)
Factor: \(5x + 25\)
1. \(5(x+5)\)
2. \(5x(1+5)\)
3. \(5(x+25)\)
4. \(25(x+1)\)
Which expression is equivalent to \(3(2y+7)\)?
1. \(6y+21\)
2. \(6y+7\)
3. \(3y+10\)
4. \(2y+21\)
Find the GCF of \(8b\) and \(20b\).
1. \(4b\)
2. \(8b\)
3. \(20b\)
4. \(2b\)
Factor: \(9m + 12\)
1. \(3(3m+4)\)
2. \(9(m+12)\)
3. \(3m(3+4)\)
4. \(12(0.75m+1)\)
Factor: \(7a + 14b\)
1. \(7(a+2b)\)
2. \(7a(1+b)\)
3. \(14(a+b)\)
4. \(a(7+14b)\)

Teacher and parent reference

Answer key and explanations

A. \(2\)
List factors: \(4\) has factors \(1, 2, 4\). \(6\) has factors \(1, 2, 3, 6\). The greatest common factor is \(2\).
A. \(2(5+3)\)
Both terms share the common factor \(2\). Factor it out: \(2 \cdot 5 + 2 \cdot 3 = 2(5+3)\).
A. \(6(x+3)\)
The GCF of \(6\) and \(18\) is \(6\). \(6x+18=6(x+3)\).
A. \(5(x+5)\)
The GCF of \(5x\) and \(25\) is \(5\). Divide both terms by \(5\) to get \(5(x+5)\).
A. \(6y+21\)
Distribute: \(3(2y+7) = 3(2y) + 3(7) = 6y+21\). Check: factor back to verify.
A. \(4b\)
Find GCF of \(8\) and \(20\): it is \(4\). Since both terms have \(b\), the GCF is \(4b\).
A. \(3(3m+4)\)
The GCF of \(9\) and \(12\) is \(3\). So \(9m+12=3(3m+4)\). (Option B confuses the constant. Option C factors only the variable. Option D uses a decimal.)
A. \(7(a+2b)\)
The GCF of \(7a\) and \(14b\) is \(7\). Factor out \(7\): \(7(a+2b)\).